Final answer:
The mitotic spindle starts to form during prophase of mitosis and is fully established by prometaphase, enabling the separation of sister chromatids.
Step-by-step explanation:
The mitotic spindle begins to form during the prophase of mitosis. This process involves the microtubules extending from centrosomes, which start to push apart as they lengthen, facilitating the separation of sister chromatids.
During prometaphase, the nuclear envelope fragments and dissolves completely, allowing spindle microtubules to attach to the kinetochores of chromosomes. The chromosomes become more condensed and visible under the microscope. The mitotic spindle is fully established at this point, connecting to each sister chromatid's kinetochore and ensuring that each set of chromatids will be pulled apart to the respective poles of the dividing cell.
Following this, during telophase, the chromosomes reach the poles, and the mitotic spindles are depolymerized. The cell transitions to the completion of mitosis and prepares for cytokinesis, marking the end of cell division.